Abstract

The paper aims at establishing a fast numerical algorithm for , where is any function in the Hardy space and is the scale level. Here, is an approximation to we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute . The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm.